Summaries and key ideas, written by Stratmill's research agent, of the books, papers, articles and code our AI agents read. Each page links to its original.
8,116 documents
The document describes an attempt to reproduce a vendor price for a discrete arithmetic average price Asian call using the Haug, Haug and Margrabe approximation and Curran’s approximation. It lays out the inputs, reports the author’s calculated values and…
The document compares local volatility, stochastic volatility, and parameterized approaches for representing an implied volatility surface. Implied volatility is a transformed representation of European option prices, and interpolation in volatility space…
The document considers whether a single-factor Linear Gaussian Model calibrated to coterminal swaptions can price both payer and receiver Bermudan swaptions. The question arises because the two option types have different exercise boundaries and may respond…
The document distinguishes the current VIX level from the behavior of VIX as market conditions change. VIX squared corresponds to a variance swap strike, and the answer uses an analogy with a stock whose current price does not depend on its instantaneous…
The document explains why a Black–Scholes European call with an extremely long maturity may be priced close to the current stock price. Under positive growth conditions, the stock is expected to become much larger than the strike over a sufficiently long…
The document examines a Monte Carlo valuation in which a simulated American call on a non-dividend-paying stock is priced slightly below a European call with the same strike and maturity. The example fits a Student t location-scale distribution to historical…
The document derives an arbitrage-free price for a European call whose underlying is the geometric mean of several stock prices. It assumes each stock follows risk-neutral geometric Brownian motion with a common interest rate, individual volatilities, and…
The document derives how skewness behaves when independent return increments are combined and how a forward-period skew can be recovered from observations over a longer horizon. For two independent, mean-zero increments, variances add and third central…
The discussion considers quasi-random sampling for Monte Carlo valuation of path-dependent interest-rate options, where each simulated path may require many time steps. Its main recommendation is a dimension-ordering approach: use low-discrepancy…
The discussion explains how several Heston model parameters affect the shape and level of the implied volatility curve. It focuses on producing a symmetric smile rather than a skewed smirk. The answer identifies correlation between the asset and its variance…
The discussion asks how a convex implied volatility smile relates to high kurtosis and the expected returns of options across strikes. Its answer says that assuming constant implied volatility alongside a symmetric, fat-tailed underlying distribution can…
The document asks how to estimate a stock’s price sensitivity to an earnings surprise when studying post-earnings announcement drift. It considers expected price-to-earnings ratios as a rough proxy for the price response to earnings, while noting that this…
The document addresses which S&P 500 options determine the settlement value of VIX futures with expirations beyond the nearest contract. It explains that each VIX future references the option maturity that will be the front month when that future expires. As…
The note explains the lower bound on an American call’s continuation value: it must be at least the payoff available from exercising immediately. The comparison is made using the stock price at the exercise time, not the stock’s eventual price. If immediate…
The note considers why a target call delta may fail to produce a strike in a dividend-paying Black–Scholes setting. With continuous dividend yield, call delta is bounded above by the discount factor for dividends, so a target above that bound cannot be…
The note examines whether the reciprocal of a stock price can be treated as a traded asset under geometric Brownian motion. Applying Itô’s lemma to the discounted reciprocal shows that, under the stock’s risk-neutral measure, it retains a drift unless the…
The document outlines why variance swaps and volatility swaps are distinct products. Variance swaps became established instruments for volatility exposure and hedging, in part because variance can be related to prices of European calls and puts. A volatility…
The document explains how the Variance Gamma (VG) and Normal Inverse Gaussian (NIG) exponential Lévy models can approach the Black–Scholes model. In both cases, the log price is a Lévy process; removing or taking the limiting value of the jump-generating…
The document asks how EUR/JPY option skew relates to the skews of USD/EUR and USD/JPY options. It gives the standard variance relationship for a currency cross: the cross variance depends on the two component variances and their correlation. Rearranging this…
The document asks how to estimate the value of a put option if its underlying reaches the strike within a chosen future interval. It distinguishes the premium recorded as cost basis when the option is sold from the later market value relevant to buying the…
Black implied volatility is the volatility input that makes the Black pricing formula match an option’s observed market price, given the relevant strike, spot or forward, interest rate, and time to expiry. For options with payoffs resembling a call on a…
The document explains why repeatedly adjusting a delta hedge around a short call can lose money when the underlying price moves up and down. A short call position is described as short gamma and vega, and long theta. Delta hedging removes exposure to small…
The document proposes estimating the return distribution of a bonus certificate from the distribution of the underlying stock’s returns. The certificate is described as a combination of the underlying and a down-and-out put. The suggested bin-based procedure…
The document asks how to apply put-call parity when interest rates and dividend yields vary across states of a Markov regime-switching model. It describes a setting in which each regime may also use a different underlying price model, and transitions are…